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Future luminosity upgrades for the LHC at CERN will require higher field magnets than those presently being utilized. The US LHC Accelerator Research Program (LARP) is addressing this need with the design and fabrication of prototype quadrupole magnets utilizing Nb3Sn technology. A part of the R&D effort is the development of suitable cables for the magnet designs being considered by LARP. The cable parameter limits for LARP prototype and production cables are presented. At present the standard strand for LARP is the Restack Rod Processed (RRP) strand being produced by Oxford Superconducting Technologies. The present strand has 54 sub-elements and 53% Cu. An optimal cable for the first generation of LARP quadrupole magnets has a width of 10 mm, thickness of 1.26 mm, and a keystone angle of 1 degree. This work shows that if a strand is properly cabled a nearly degradation-free mechanically-stable cable can be produced.